A note on oscillation modulus of PL-process and its applications under random censorship

The strong limit results of oscillation modulus of PL-process are established in this paper when the density function is not continuous function for censored data. The rates of convergence of oscillation modulus of PL-process are sharp under week condition. These results can be used to derive laws of the iterated logarithm of random bandwidth kernel estimator and nearest neighborhood estimator of density under continuous conditions of density function being not assumed.